OFFSET
1,1
COMMENTS
This sequence is infinite, assuming Schinzel's Hypothesis H.
Related to Rassias Conjecture ("for any odd prime p there are primes q < r such that p*q = q + r + 1") setting p = q. Generalization can be achieved by removing semiprimality condition and accepting p^e, e >= 2.
These are semiprimes m = p*q such that 1/p + 1/q - 1/m = p/q. Cf. A326690. - Amiram Eldar and Thomas Ordowski, Jul 22 2019
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..10000
For Rassias conjecture: Preda Mihăilescu, Review of Problem Solving and Selected Topics in Number Theory, Newsletter of the European Mathematical Society, March 2011, p. 46.
EXAMPLE
a(1) = 6 = 2*3 = 2*(2^2-2+1).
a(2) = 21 = 3*7 = 3*(3^2-3+1).
a(3) = 301 = 7*43 = 7*(7^2-7+1).
MAPLE
seq(`if`(isprime((ithprime(i)^2-ithprime(i)+1))=true, (ithprime(i)^2-ithprime(i)+1)*ithprime(i), NULL), i=1..300);
MATHEMATICA
p = Select[Prime@ Range@ 500, PrimeQ[#^2 - # + 1] &]; p (p^2 - p + 1) (* Giovanni Resta, Jul 22 2019 *)
PROG
(PARI) forprime(p=2, 1e4, if(isprime(k=p^2-p+1), print1(p*k", "))) \\ Charles R Greathouse IV, May 08 2011
CROSSREFS
KEYWORD
nonn
AUTHOR
Giorgio Balzarotti, May 07 2011
STATUS
approved